Q77 / 90 · JEE Main 2024 (08 Apr Shift 2) · Physics

Two satellite $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $\mathrm{A}$ is $3 v$, the speed of $\mathrm{B}$ will be :

  • A
    $3 v$
  • Correct answer
    B
    $6 v$
  • C
    $\frac{4}{3} v$
  • D
    $12 v$

Solution

$\begin{aligned} & \mathbf{v}=\sqrt{\frac{G M}{R}} \\ & \frac{v_A}{v_B}=\sqrt{\frac{R_B}{R_A}}=\sqrt{\frac{R}{4 R}}=\frac{1}{2} \\ & v_B=2 v_A=6 v\end{aligned}$

Hence, the correct answer is option: 'B'.

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